Hence , the diameter of the trunk of the tree is 2.54 × 10⁻¹ m which is option (B) .
An equation could be a statement, that has associate equal sign (=) between the pure mathematics expression. Linear equations area unit the equations of degree one. it's the equation for the line. The solutions of linear equations can generate values, that once substituted for the unknown values, build the equation true.Let the diameter of stem of a flower be " x" and diameter of the trunk of a tree be " y " .
According to the question "The diameter of the trunk of a tree is 40 times greater than the stem of the flower " which can be represented by
y = 40 x .....(1)
It is given that stem of a flower has a diameter of 6.35 × 10⁻³ meters.
Putting x = 6.35 × 10⁻³ in equation (1) , we get
y = 40 × 6.35 × 10⁻³
y = 254 × 10⁻³
y = 2.54 × 10⁻¹ m
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The drying time of one particular paint is approximately normally distributed with a mean of 45
minutes. It is also known that 15% of walls painted with this paint need more than 55 minutes to
dry completely. Find the standard deviation of this distribution.
The standard deviation of this distribution is 9.65 minutes.
Due to its description in terms of the second central moment, the standard deviation naturally arises in mathematical statistics.
Any distribution with finite first two moments can have its standard deviation defined, although the most common assumption is that the underlying distribution is normal.
In the above given question it is stated that:
mean(μ) of the distribution is 45 and let us consider the standard deviation to be σ
We convert this to standard normal as
[tex]P(X < x) = P(Z < \frac{( x - \mu)} {\sigma})[/tex]
We have , P(X > 55) = 0.15 (15%)
This can be simplified as:
P(X < 55) = 1 - 0.15
P(X < 55) = 0.85
[tex]P(Z < \frac{( x - \mu)} {\sigma}) = 0.85[/tex]
From Z table, z-score for the probability of 0.85 is found out to be 1.0364 ,
therefore :
[tex]\frac{( 55 - 45)}{ \sigma }= 1.0364\\\\ \sigma = ( 55 - 45) / 1.0364 \\\\\sigma = 9.65[/tex]
Hence the standard deviation is 9.65 minutes.
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What set of reflections and rotations would carry rectangle ABCD onto itself?
Reflect over the y-axis, reflect over the x-axis, rotate 180°
Rotate 180°, reflect over the x-axis, reflect over the line y = x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y = x
Answer:
2 line is the answer to the questions
please help me again!! i’m probably not focusing because i’m tired.
Answer: x=14
Step-by-step explanation:
First let's find all the inner angles of the triangle.
124+DCB=180 ==> Angles DCB and 124 lie on a straight line. Straight lines measure 180 degrees and are called straight angles.
124+DCB=180
124-124+DCB=180-124
DCB=180-124
DCB=56 degrees
6x+CBD=180 ==> straight angle
2x+CBD+56=180 ==> total degrees of a triangle is 180 degrees
6x+CBD=2x+CBD+56 ==> they both equal 180
6x+CBD-CBD=2x+CBD-CBD+56
6x=2x+56
6x-2x=2x-2x+56
4x=56
4x/4=56/4
x=14
Can yall help me with this
From the values that we have the magnitude of the value of the stock A would be given as 4.15. Option A is correct.
What is the magnitude of a stock?This is the term that is sued to refer to how far the run of a particular stock is in terms of its price. In order to get the magnitude, we would have to find the absolute value of the stock A as we have it here.
Remember the absolute value would have to change the value to be positive if it was negative.
Hence we would have
I-4.15I = 4.15
Hence the solution is 4.15
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Suppose you toss a coin four times. What is the probability of getting four tails?
Answer:
1/16
Step-by-step explanation:
Coin toss
probability 1/2×1/2×1/2×1/2 = 1/16
Need help finding x please
Answer:
[tex]x = \frac{64}{3} [/tex]
Step-by-step explanation:
Based on the given conditions:
[tex] \frac{x}{32} = \frac{12}{12 + 6} ⟹ \frac{x}{32} = \frac{12}{18} [/tex]
Cross multiply the above
[tex]18x = 384 [/tex]
Divide both sides by 18 to find the value of x
[tex]x = \frac{384}{18} [/tex]
Therefore:
[tex]x = \frac{64}{3} [/tex]
if the car continues at the same accerleration meaning the slope of the line does not change how fast would it be going in 15 seconds
The car's velocity after 15 seconds is 60.3 m/s.
What is velocity?Velocity is the directional speed of a moving object as an indication of its rate of change in position as observed from a specific frame of reference and measured by a specific time standard.The linear regression equation obtained by fitting the data using technology is:
y = 3.64x + 5.7x = times(seconds) ; y = velocity(m/s)The approximate velocity at time = 0 and x = 0 is as follows:
y = 3.64(0) + 5.7y = 0 + 5.7y = 5.7 m/sAfter 15 seconds, the velocity is:
At time, x = 15 secondsy = 3.64(15) + 5.7y = 60.3 m/sTherefore, the car's velocity after 15 seconds is 60.3 m/s.
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Which product is NOT equal to 13 ?
a. (4+√3 )(4-√3 )
b. (5-2 √3 )(5+2 √3 )
c. (6+√23 )(6-√23 )
d. (7-√6 )(7+√6 )
Answer:
the answer is D
Step-by-step explanation:
because it gives us 43 as the answer
Write an equation of each line in point-slope form.
(-4,-3) and (2,7
The equation of the line in point-slope form, which passes through the pair of points located at (-4 , -3) and (2 , 7), is y + 3 = 5/3(x + 4).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Getting the slope of the two points: (-4 , -3) and (2 , 7).
m = (y2 - y1)/(x2 - x1)
m = (7 - -3)/(2 - -4)
m = 10/6
m = 5/3
Using the point slope form, plug in the values of the slope and Point A to set up the equation.
(y - y1) = m(x - x1)
where m = 5/3 and (x1 , y1) = (-4 , -3)
(y - -3) = 5/3(x - -4)
y + 3 = 5/3(x + 4)
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Which graph represents a function with amplitude 4 and period π?
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at pi.
On a coordinate plane, a cosine function has a maximum of 2 and minimum of negative 2. It completes one period at 2 pi.
On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
The correct option is On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
What is amplitude?The maximum displacement or distance moved by a point on a vibrating body or wave measured from its equilibrium position.
Given:
function with amplitude 4 and period π.
also, The period of a wave is the time for a particle on a medium to make one complete vibrational cycle.
so, the amplitude 4 means function has a maximum of 4 and minimum of negative 4.
Hence, On a coordinate plane, a cosine function has a maximum of 4 and minimum of negative 4. It completes one period at pi.
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Answer:
D
Step-by-step explanation:
just took it
There are n socks, 3 of which are red, in a drawer. what is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12 ?
n=4 is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12.
What is the probability in simple terms?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Number of socks = n .
Number of red socks = 3 .
Given
3C2nC2=12
⇒nC2=3×2=6
⇒n=4
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5 Granola bars cost $4.00
b. Fill in the table that shows the
costs for 10, 15, and
20 granola bars. Find the cost for a
single granola bar in each case.
Answer:
1 granola bar =
Step-by-step explanation:
10 granola bars= $4.00 x 2 = $8.00
15 granola bars=$4.00 x 3 = $12.00
20 granola bars=$4.00 x 4 = $16.00
1 granola bar = $0.80p
what can 6 divided by using a -1/2?
If the distance between Earth and the Sun is actually 150,000,000 kilometers, how far apart are Earth and the Sun when using the 1:93,000,000 scale model?
The scaled distance using the given scale factor is; 1.613 units
How to use the scale model?
We are given;
Distance between Earth and the sun = 150, 000, 000 km
Now, we are given that the scale model that represents Distance between Earth and the sun is 1:93,000,000.
This means that 1 unit represents 93000000 kilometers. Thus;
The scaled distance using the given scale factor is;
150,000,000/93,000,000 = 1.613 units
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Determine the distance between the points (c,d) and (0,0). Answer of terms of c and d
Answer:
Step-by-step explanation:
(y2-y1)/(x2-x1)
(0-d)/(0-c)
-d/-c
d/c
Find each difference.
-16-(-25)
The difference is 9.
How to find the difference?A difference is a result of subtracting two numbers.
It speaks of the difference in quantity between two numbers.
Given,
-16-(-25)
Solution:
Since (-) + (-) = +
-16-(-25) = -16 + 25
= 9
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-7x+4=-128+4x
with work pls :D
Answer:
Step-by-step explanation:
Rearrange terms -7x+4=4x-128 subtract 4 from both sides. Simplify . subtract 4x from both sides. simplify. divide both sides by the same factor. simplify. Solution x=12
2(-4)² + (-4)³ +24 - 18(-12)2
Answer:
-440
Step-by-step explanation:
Simplify
2(-4)^2+(-4)^3+24-18(-12)2
2(16)+(-64)+24-432
32-64+24-432
-440
50 PTS - Functional Notation. Please explain how to do this!
9+6.6x=7x-8.7
Help me solve it please
Answer:
x = 44.25
Step-by-step explanation:
9 + 6.6x = 7x - 8.7
-7x -7x
---------------------------
9 - 0.4x = -8.7
-9 -9
-0.4x = -17.7
÷-0.4 ÷-0.4
-------------------
x = 44.25
c. What do you notice about these three angles?
Answer:
Added all up, they will form 180 degrees aka a straight line.
Step-by-step explanation:
To find S, just add 45 + 80. We get 125. Then, subtract 125 from 180!
S = 55 :)
Simplify each rational expression. State any restrictions on the variable. c²-8 c+12 / c²-11 c+30
Simplify each rational expression. State any restrictions on the variable.
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\frac{(c-2)}{(c-5)}[/tex]
How the rational expression is simplified?
[tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }\\\\= > \frac{(c-2)(c-6)}{(c-5)(c-6)} \\= > \frac{(c-2)}{(c-5)}[/tex]
What are the restrictions on the variable ?
If c= 5 , the denominator becomes,
[tex]c^{2} -11c+30[/tex] =25-55+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
If c= 6 ,the denominator becomes,
[tex]c^{2} -11c+30[/tex] = 36- 66+30=0
⇒ [tex]\frac{c^{2}-8c+12 }{c^{2}-11c+30 }=\infty[/tex]
So, the restrictions on the variable are: c≠ 5,6
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Find the value of x and y.
Answer:
9. x = 10310. x = 50Step-by-step explanation:
9)
x + x - 26 = 180
2x = 180 + 26
2x = 206
x = 206 : 2
x = 103
check
103 + 103 - 26 = 180
180 = 180
the answer is good
10.
2x - 40 = x + 10
x = 40 + 10
x = 50
check
2 * 50 - 40 = 50 + 10
60 = 60
the answer is good
The graph shows the cube root parent function. Which statement is true? A. (0, 1) is the x and y-intercept of the function. B. The function has no intercepts. C. (1, 1) is the x and y-intercept of the function. D. (0,0) is the x and y-intercept of the function.
Answer:
D
Step-by-step explanation:
X and y come together at (0,0) right?
Write an explicit formula for each geometric sequence. 25,5,1, 1/5, . . .
The explicit formula is [tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
For the Geometric sequence, the explicit formula for the nth term is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where,
a = first number of the series
r = common ratio
n = number of series
[tex]a_{1}[/tex] = a
[tex]a_{2}[/tex] = ar
[tex]a_{3}[/tex] = a [tex]r^{2}[/tex]
.....
Therefore the series is a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],,,,.....
Here we have the series 25, 5, 1, 1/5
Here common ratio = 1/5
and if we want to find the 5th term the formula is
[tex]a_{5}[/tex] = 25 ×[tex](\frac{1}{5} )^{4}[/tex]
= [tex]\frac{1}{25}[/tex]
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A company rents out 14 food booths and 21 game booths at the county fair. The fee for a food booth is $175 plus $9 per day. The fee for a game booth is $50 plus $8 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount, in dollars, that the company is paid.
A simplified expression for the amount, in dollars, that the company is paid is $3,500+273d.
Given that, a company rents out 14 food booths and 21 game booths at the county fair. The fee for a food booth is $175 plus $9 per day. The fee for a game booth is $50 plus $8 per day.
What is an expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given, the fair lasts for d days, and all the booths are rented for the entire time.
So, Food Booth Fee can be calculated as follows:
14(175+9d)
=2,450+126d
Game Booth Fee can be calculated as follows:
=21(50+8d)
=1050+168d
So, the total Food and Game Booth Fees:
=2,450+126d+1050+168d
=3,500+273d
Therefore, a simplified expression for the amount, in dollars, that the company is paid is $3,500+273d.
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Your teacher asks you to find a recipe that includes two ingredients with a ratio of 1/2 over one 1/8 cup . Give an example of two ingredients in a recipe that would meet this requirement
The recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
The example is with flour and sugar
Let
x = the number of cups of flour
y = the number of cups of sugar
We know that:
Ratio means the comparison between the two values.
Ratio = x / y
Now, we can let
x = 1 / 2 cups of flour
y = 1 / 8 cups of sugar
Ratio will be
= 1 / 2 : 1 / 8
= 8 : 2
= 4 : 1
Therefore, the recipe of flour and sugar can be given as an example where we will get the ratio as 4 : 1.
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PART 2!!
Topic: Addition and Subtraction of polynomials
Directions: Simplify each rational expressions
Step-by-step explanation:
4.
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] \: [/tex]
5.
[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]
[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]
[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]
[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]
[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]
[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve these problems ~
Problem 1 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
Problem 2 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]
[ taking 2 common out ]
[tex]{ \qquad \sf \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]
In the first half football season, Marco ran 4 plays for a gain of 60 yards. During the second half of the season, Marco was responsible for 6 penalties resulting in a loss of 80 yards. What was his total yardage for his football season?
i can't figure this out
2/3(x-3)+6x
Step-by-step explanation:
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